1. Define the following terms in your own words: (a) hypothesis-testing procedure, (b) .05 significance level, and (c) two-tailed test.
2. List the five steps of hypothesis testing, and explain the procedure and logic of each.
1.
2.
3.
4.
5.
3. Based on the information given for each of the following studies, decide whether to reject the null hypothesis. For each, give (a) the Z-score cutoff (or cutoffs) on the comparison distribution at which the null hypothesis should be rejected, (b) the Z score on the comparison distribution for the sample score, and (c) your conclusion. Assume that all populations are normally distributed.
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Population |
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Study |
μ |
σ |
Sample Score |
p |
Tails of Test |
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A |
5 |
1 |
7 |
.05 |
1 (high predicted) |
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B |
5 |
1 |
7 |
.05 |
2 |
|
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C |
5 |
1 |
7 |
.01 |
1 (high predicted) |
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D |
5 |
1 |
7 |
.01 |
2 |
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1. A. B. C.
2. A. B. C.
3. A. B. C.
4. A. B. C.
4. Evolutionary theories often emphasize that humans have adapted to their physical environment. One such theory hypothesizes that people should spontaneously follow a 24-hour cycle of sleeping and waking—even if they are not exposed to the usual pattern of sunlight. To test this notion, eight paid volunteers were placed (individually) in a room in which there was no light from the outside and no clocks or other indications of time. They could turn the lights on and off as they wished. After a month in the room, each individual tended to develop a steady cycle. Their cycles at the end of the study were as follows: 25, 27, 25, 23, 24, 25, 26, and 25. Using the .05 level of significance, what should we conclude about the theory that 24 hours is the natural cycle? (That is, does the average cycle length under these conditions differ significantly from 24 hours?) (a) Use the steps of hypothesis testing. (b) Sketch the distributions involved, (c) Explain your answer to someone who has never taken a course in statistics.
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6. Do students at various universities differ in how sociable they are? Twenty-five students were randomly selected from each of three universities in a region and were asked to report on the amount of time they spent socializing each day with other students. The result for University X was a mean of 5 hours and an estimated population variance of 2 hours; for University Y, M = 4, S2 = 1.5; and for University Z, M = 6, S2 = 2.5. What should you conclude? Use the .05 level. (a) Use the steps of hypothesis testing, (b) figure the effect size for the study; and (c) explain your answers to parts (a) and (b) to someone who has never had a course in statistics.
a. Make up a scatter diagram with 10 dots for each of the following situations:
b. perfect positive linear correlation,
c. large but not perfect positive linear correlation,
d. small positive linear correlation,
e. large but not perfect negative linear correlation,
f. no correlation,
g. clear curvilinear correlation.
7.
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7. Four research participants take a test of manual dexterity (high scores mean better dexterity) and an anxiety test (high scores mean more anxiety). The scores are as follows.
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